Finally making argument for increase (4)
I believe the answer is:
grow
'for increase' is the definition.
(growing is a kind of increasing)
'finally making argument' is the wordplay.
'finally' suggests the final letters.
'argument' becomes 'row' (to row is to argue).
The last letter of 'making' is 'g'.
'g'+'row'='GROW'
(Other definitions for grow that I've seen before include "Wax" , "Develop - propagate" , "Become bigger" , "Get bigger" , "Burgeon" .)